Generalized Shapley Choquet Integral Operator Based Method for Interactive Interval-Valued Hesitant Fuzzy Uncertain Linguistic Multi-Criteria Group Decision Making

This paper develops a new method based on generalized hybrid Shapley Choquet integral for interval-valued hesitant fuzzy uncertain linguistic multi-criteria group decision making (MCGDM), where interactive characteristics of criteria is taken into account. First, a score function and a new accuracy function are defined to rank the interval-valued hesitant fuzzy uncertain linguistic elements (IVHFULEs). Based on the Shapley Choquet integral, some generalized Shapley Choquet operator for IVHFULEs are proposed including an interval-valued hesitant fuzzy uncertain linguistic generalized Shapley Choquet (IVHFULGSC) operator and an interval-valued hesitant fuzzy uncertain linguistic generalized hybrid Shapley Choquet (IVHFULGHSC) operator and some attractive properties for these two operators are investigated in detail. Then a Shapley Choquet integral-based Minkowski distance between interval-valued hesitant fuzzy uncertain linguistic sets (IVHFULSs) is defined. Subsequently, based on the maximization deviation method, a linear programming model is built to determine the individual fuzzy measure on criteria set for each decision maker (DM). By utilizing the individual closeness coefficients matrices, a new multi-objective fractional programming model which maximizes the collective relative closeness degrees of all alternatives is constructed to obtain the fuzzy measure on DMs set. The individual decision matrices are aggregated into the collective one by using the IVHFULGHSC operator. To obtain the collective Shapely fuzzy measure on criteria set, a linear programming model is established by maximizing the deviation of the evaluations of different alternatives on each criterion. Then, the collective closeness coefficients of alternatives are calculated to rank the alternatives. Thus, a new method based on generalized hybrid Shapley Choquet integral operator is brought forward for MCGDM with IVHFULEs. Finally, an example of investment on shared bikes is provided to illustrate the applicability of the proposed method and a validity test is conducted to demonstrate the effectiveness of the proposed method.